Mathematical modeling and computer simulations are widely used to predict the behavior of complex biological phenomena. However, increased computational resources have allowed scientists to ask a deeper question, namely, "how do the uncertainties ubiquitous in all modeling efforts affect the output of such predictive simulations?" Examples include both epistemic (lack of knowledge) and aleatoric (intrinsic variability) uncertainties and encompass uncertainty coming from inaccurate physical measurements, bias in mathematical descriptions, as well as errors coming from numerical approximations of computational simulations. Because it is essential for dealing with realistic experimental data and assessing the reliability of predictions based on numerical simulations, research in uncertainty quantification (UQ) ultimately aims to address these challenges.

Uncertainty quantification (UQ) uses quantitative methods to characterize and reduce uncertainties in mathematical models, and techniques from sampling, numerical approximations, and sensitivity analysis can help to apportion the uncertainty from models to different variables. Critical to achieving validated predictive computations, both forward and inverse UQ analysis have become critical modeling components for a wide range of scientific applications. Techniques from these fields are rapidly evolving to keep pace with the increasing emphasis on models that require quantified uncertainties for large-scale applications.
This tutorial focused on the application of these methods and techniques to mathematical models in the life sciences and provided researchers with the basic concepts, theory, and algorithms necessary to quantify input and response uncertainties and perform sensitivity analysis for simulation models. Concepts covered included: probability and statistics, parameter selection techniques, frequentist and Bayesian model calibration, propagation of uncertainties, quantification of model discrepancy, adaptive surrogate model construction, high-dimensional approximation, random sampling and sparse grids, as well as local and global sensitivity analysis.

This tutorial was intended for graduate students, postdocs and researchers in mathematics, statistics, computer science and biology. A basic knowledge of probability, linear algebra, and differential equations was assumed.

Live Stream.
The Tutorial was streamed live. A live chat took place via Twitter with the hashtag #uncertaintyTT.
Selected presentation videos will be available online soon.

A goal of NIMBioS is to enhance the cadre of researchers capable of interdisciplinary efforts across mathematics and biology. As part of this goal, NIMBioS is committed to promoting diversity in all its activities. Diversity is considered in all its aspects, social and scientific, including gender, ethnicity, scientific field, career stage, geography and type of home institution. Questions regarding diversity issues should be directed to Dr. Ernest Brothers, the NIMBioS Associate Director for Diversity Enhancement (diversity@nimbios.org). You can read more about our Diversity Plan on our NIMBioS Policies web page. The NIMBioS building is fully handicapped accessible.

NIMBioS is sponsored by the
National Science Foundation
through NSF Award #DBI-1300426, with additional support from
The University of Tennessee, Knoxville.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.